Now that Bill has been introduced, we move on to her first proper adventure in the form of “Smile,” novelist and screenwriter Frank Cottrell-Boyce’s second contribution to the show.

The episode kicks off with a bit of a Tardis console tour and a discussion of the vessel’s theft and value. The suggestion that Bill, or any companion, could steal a Tardis might at first seem unlikely, but isn’t that exactly what Clara and Me did in last year’s finale?

We are introduced to Nardole in full-on “Mum” mode, reminding the Doctor of his responsibilities and, by putting the kettle on in readiness to pour the tea, he is literally embodying the idiom of “being mother.”

As fortunate as the show is to have Matt Lucas as a regular cast member, and as much as I said last week that I wanted to see his character given more to do, I am actually glad to see him side-lined this week. Lucas is a massive comedy star, but with mass comes a further comedic gravity that warps every scene in which he appears as the audience watches attentively for any amusing line or gesture he might make.

Getting Lucas’s Nardole out of the Tardis for a bit gives both Pearl Mackie and her character more of a chance to shine, and shine she does, with excitement and gratitude for a day out that is truly out-of-this-world.

Shortly after Bill gets off-world, we are treated to a bit of a recap of the season’s central mystery. Doctor confirms just about everything we don’t know so far about the vault in the university’s basement. As the Doctor says, “A long time ago, a thing happened, as a result of the thing, I made a promise, as the result of the promise I have to stay on Earth,” specifically to guard a vault.

I’m not going to speculate what lies behind its doors right now, mainly because I suspect the answer might be “nothing.” Only time will tell.

Back to this week’s adventure, the on-location shooting at the City of Arts and Sciences in Valencia really sells the story’s alien world setting. Spain is just about as far from the standard-issue British quarry planet of the classic series as you can get.

There are no monsters, only the Vardi, little insect-like robots that fly around in swarms, join together to form modern-looking architecture and that communicate with humans via emoji-spouting humanoid interfaces.

The Doctor’s claim here that “no other species in the universe uses emojis” struck me as more than a little odd, if not outright wrong. Emojis are pictographic language – from a design perspective, a face composed of two dots is more universally applicable than any abstract text-based language, especially in the Doctor Who universe, where most aliens do actually have two eyes and a mouth. Wouldn’t a Cyberman or an Ice Warrior, or any number of other alien species be able to recognize a simple line drawing of a face?

Back to the plot, the Vardi were supposed to build facilities for an incoming group of human colonists, and ensure their future comfort and happiness. Unfortunately, they became a little too single-minded in pursuit of their goal and ended up killing anyone who looked at all unhappy.

In an attempt to placate the Vardi, The Doctor attempts to deploy some David Bowie lyrics from Ashes to Ashes, smiling and saying “I’m Happy, Hope you’re happy too,” although the Charlie Chaplin, John Turner and Geoffrey Parsons tune “Smile” might be more appropriate. “Smile, though your heart is breaking,” indeed.

Where the episode really works for me is in the idea that the Doctor has made a mistake, or rather two: thinking that the colonists are still on their way, instead of hibernating in their already-arrived ship, and thinking that the robots were a non-sentient enemy rather than an emergent life form. Most importantly of all, the Doctor then works hard to actively make amends for his errors.

Some might quibble that the name of the colony ship, the Erehwon is a little on the nose for a story about the non-existence of utopias. They also might be unhappy that the Doctor’s solution to the Vardi problem is to literally hit the reset button, resulting in the robots loosing both their memories and their assumptions about the relative merits of killing unhappy people. For me, the button’s use felt justified, like it had been earned by the Doctor admitting owning his own screw-ups.

And speaking of screw-ups, the episode ends with the Doctor failing to get back to The Vault in time for tea, but instead heading back London during the early 1800s. The idea of Bill wandering around Regency England during a great frost fair has definitely got me looking forward to next week already.